Interferometric technique for quantitating biological indicators

ABSTRACT

A technique is described for quantitating biological indicators, such as viral load, using interferometric interactions such as quantum resonance interferometry. A diffusion curve for the biological indicator of interest is generated from at least two measurements from a patient sample. In some embodiments, the patient samples are in the form of a microarray output pattern to which the patient sample has been applied. After the diffusion curve has been generated, subsequent patient samples are mapped to the diffusion curve to provide a quantitative measure of the biological indicator of interest.

[0001] This application is a Continuation of U.S. patent applicationSer. No. 10/189,885 entitled “Technique for Quantitating BiologicalMarkers Using Quantum Resonance Interferometry” which is a Continuationof U.S. patent application Ser. No. 09/523,539 entitled “Method andSystem for Quantitation of Viral Load Using Microarrays” filed Mar. 10,2000, which is a Continuation of U.S. patent application Ser. No.09/253,791, now U.S. Pat. No. 6,245,511, entitled “Method and Apparatusfor Exponentially Convergent Therapy Effectiveness Monitoring Using DNAMicroarray Based Viral Load Measurements” filed Feb. 22, 1999, all ofwhich are hereby incorporated by reference.

FIELD OF THE INVENTION

[0002] The invention generally relates to techniques for monitoring theeffectiveness of medical therapies and dosage formulations, and inparticular to techniques for monitoring therapy effectiveness usingviral load measurements.

BACKGROUND OF THE INVENTION

[0003] It is often desirable to determine the effectiveness oftherapies, such as those directed against viral infections, includingtherapies involving individual drugs, combinations of drugs, or otherrelated therapies. One conventional technique for monitoring theeffectiveness of a viral infection therapy is to measure and track aviral load associated with the viral infection, wherein the viral loadis a measurement of a number of copies of the virus within a givenquantity of blood, such per milliliter of blood. The therapy is deemedeffective if the viral load is decreased as a result of the therapy. Adetermination of whether any particular therapy is effective is helpfulin determining the appropriate therapy for a particular patient and alsofor determining whether a particular therapy is effective for an entireclass of patients. The latter is typically necessary in order to obtainFDA approval of any new drug or medical device therapy. Viral loadmonitoring is also useful for research purposes such as for assessingthe effectiveness of new antiviral compounds determine, for example,whether it is useful to continue developing particular antiviralcompounds or to attempt to gain FDA market approval.

[0004] A test to determine the viral load can be done with blood drawnfrom T-cells or from other standard sources. The viral load is typicallyreported either as an absolute number, i.e., the number of virusparticles per milliliter of blood or on a logarithmic scale. Likewise,decreases in viral load are reported in absolute numbers, logarithmicscales, or as percentages.

[0005] It should be noted though that a viral load captures only afraction of the total virus in the body of the patient, i.e., it tracksonly the quantity of circulating virus. However, viral load is animportant clinical marker because the quantity of circulating virus isthe most important factor in determining disease outcome, as changes inthe viral load occur prior to changes in other detectable factors, suchas CD4 levels. Indeed, a measurement of the viral load is rapidlybecoming the acceptable method for predicting clinical progression ofcertain diseases such as HIV.

[0006] Insofar as HIV is concerned, HIV-progression studies haveindicated a significant correlation between the risk of acquiring AIDSand an initial HIV baseline viral load level. In addition to predictingthe risk of disease progression, viral load testing is useful inpredicting the risk of transmission. In this regard, infectedindividuals with higher viral load are more likely to transmit the virusthan others.

[0007] Currently, there are several different systems for monitoringviral load including quantitive polymerase chain reaction (PCR) andnucleic acid hybridization. Herein, the term viral load refers to anyvirological measurement using RNA, DNA, or p24 antigen in plasma. Notethat viral RNA is a more sensitive marker than p24 antigen. p24 antigenhas been shown to be detectable in less than 50% asymptomaticindividuals. Moreover, levels of viral RNA rise and fall more rapidlythan levels of CD4+ lymphocytes. Hence, changes in infection can bedetected more quickly using viral load studies based upon viral RNA thanusing CD4 studies. Moreover, viral load values have to date proven to bean earlier and better predictor of long term patient outcome thanCD4-cell counts. Thus, viral load determinations are rapidly becoming animportant decision aid for anti-retro viral therapy and diseasemanagement. Viral load studies, however, have not yet completelyreplaced CD+ analysis in part because viral load only monitors theprogress of the virus during infection whereas CD4+ analysis monitorsthe immune system directly. Nevertheless, even where CD4+ analysis iseffective, viral load measurements can supplement information providedby the CD4 counts. For example, an individual undergoing long termtreatment may appear stable based upon the observation of clinicalparameters and CD4 counts. However, the viral load of the patient maynevertheless be increasing. Hence, a measurement of the viral load canpotentially assist a physician in determining whether to change therapydespite the appearance of long term stability based upon CD4 counts.

[0008] Thus, viral load measurements are very useful. However, thereremains considerable room for improvement. One problem with currentviral load measurements is that the threshold level for detection, i.e.,the nadir of detection, is about 400-500 copies per milliliter. Hence,currently, if the viral load is below 400-500 copies per milliliter, thevirus is undetectable. The virus may nevertheless remain within thebody. Indeed, considerable quantities of the virus may remain within thelymph system. Accordingly, it would be desirable to provide an improvedmethod for measuring viral load which permits viral load levels of lessthan 400-500 copies per milliliter to be reliably detected.

[0009] Another problem with current viral load measurement techniques isthat the techniques are typically only effective for detectingexponential changes in viral loads. In other words, current techniqueswill only reliably detect circumstances wherein the viral load increasesor decreases by an order of magnitude, such by a factor of 10. In othercases, viral load measurements only detect a difference betweenundetectable levels of the virus and detectable levels of the virus. Ascan be appreciated, it would be highly desirable to provide an improvedmethod for tracking changes in viral load which does not require anexponential change in the viral load for detection or which does notrequire a change from an undetectable level to a detectable level.Indeed, with current techniques, an exponential or sub-exponentialchange in the viral load results only in a linear change in theparameters used to measure the viral load. It would instead be highlydesirable to provide a method for monitoring the viral load whichconverts a linear change in the viral load into an exponential changewithin the parameters being measured to thereby permit very slightvariations in viral load to be reliably detected. In other words,current viral load detection techniques are useful only as a qualitativeestimator, rather than as a quantative estimator.

[0010] One reason that current viral load measurements do not reliablytrack small scale fluctuations in the actual number of viruses is that asignificant uncertainty in the measurements often occurs. As a result,individual viral load measurements have little statistical significanceand a relatively large number of measurements must be made before anystatistically significant conclusions can be drawn. As can beappreciated it would be desirable to provide a viral load detectiontechnique which can reliably measure the viral load such that thestatistical error associated with a single viral load measurement isrelatively low to permit individual viral load measurements to be moreeffectively exploited.

[0011] Moreover, because individual viral load measurements are notparticularly significant when using current methods, treatment decisionsfor individual patients based upon the viral load measurements must bebased only upon long term changes or trends in the viral load resultingin a delay in any decision to change therapy. It would be highlydesirable to provide an improved method for measuring and tracking viralload such that treatment decisions can be made much more quickly basedupon short term trends of measured viral load.

[0012] As noted above, the current nadir of viral load detectability isat 400-500 copies of the virus per milliliter. Anything below that levelis deemed to be undetectable. Currently the most successful and potentmulti-drug therapies are able to suppress viral load below that level ofdetection in about 80-90 percent of patients. Thereafter, viral load isno longer an effective indicator of therapy. By providing a viral loadmonitoring technique which reduces the nadir of detectabilitysignificantly, the relative effectiveness of different multi-drugtherapies can be more effectively compared. Indeed, new FDA guidelinesfor providing accelerated approval of a new drug containing regimenrequires that the regimen suppress the viral load below the currentnadir of detection in about 80 to 85 percent of cases. If the newregimen suppresses the viral load to undetectable levels in less than 80to 85 percent of the cases, the new drug will gain accelerated approvalonly if it has other redeeming qualities such as a preferable dosingregimen (such as only once or twice per day), a favorable side effectprofile, or a favorable resistance or cross-resistance profile. Thus,the ability of a regimen to suppress the viral load below the level ofdetection is an important factor in FDA approval. However, because thelevel of detectability remains relatively high, full approval iscurrently not granted by the FDA solely based upon the ability of theregimen to suppress the viral load below the minimum level of detection.Rather, for full approval, the FDA may require a further demonstrationof the durability of the regimen, i.e., a demonstration that the drugregimen suppresses the viral load below the level of detectability andkeeps it below the level of detectability for some period of time.

[0013] As can be appreciated, if a new viral load measurement andtracking technique were developed which could reliably detect viral loadat levels much lower than the current nadir of detectability, the FDAmay be able, using the new technique, to much more precisely determinethe effectiveness of a drug regimen for the purposes of grantingapproval such that a demonstration of the redeeming evalities will nolonger be necessary.

[0014] For all of these reasons, it would be highly desirable to providean improved technique for measuring and tracking viral load capable ofproviding much more precise and reliable estimates of the viral load andin particular capable of reducing the nadir of detectabilitysignificantly. The present invention is directed to this end.

SUMMARY OF THE INVENTION

[0015] In accordance with a first aspect of the invention, a method isprovided for determining the effectiveness of a therapy, such as ananti-viral therapy, by analyzing biochip output patterns generated frombiological samples taken at different sampling times from a patientundergoing the therapy. In accordance with the method, a viral diffusioncurve associated with a therapy of interest is generated and each of theoutput patterns representative of hybridization activity is then mappedto coordinates on the viral diffusion curve using fractal filtering. Adegree of convergence between the mapped coordinates on the viraldiffusion curve is determined. Then, a determination is made as towhether the therapy of interest has been effective based upon the degreeof convergence.

[0016] In an exemplary embodiment, the viral diffusion curve isspatially parameterized such that samples map to coordinates near thecurve maxima, if the viral load is increasing (i.e., therapy or dosageis ineffective). In this manner, any correlation between rate and extentof convergence across different patient samples is exploited to providea quantitative and qualitative estimate of therapy effectiveness.

[0017] Also in the exemplary embodiment, the biological sample is a DNAsample. The output pattern of the biochip is quantized as a dotspectrogram. The viral diffusion curve is generated by inputtingparameters representative of viral load studies for the therapy ofinterest, generating a preliminary viral diffusion curve based upon theviral load studies; and then calibrating a degree of directionalcausality in the preliminary viral diffusion curve to yield the viraldiffusion curve. The parameters representative of the viral load studiesinclude one or more of baseline viral load (BVL) set point measurementsat which detection is achieved, BVL at which therapy is recommended andviral load markers at which dosage therapy is recommended. The step ofgenerating the preliminary viral diffusion curve is performed byselecting a canonical equation representative of the viral diffusioncurve, determining expectation and mean response parameters for use inparameterizing the equation selected to represent the viral diffusioncurve and parameterizing the equation selected to represent the viraldiffusion curve to yield the preliminary viral diffusion curve.

[0018] Also, in the exemplary embodiment, each dot spectrogram is mappedto the viral diffusion curve using fractal filtering by generating apartitioned iterated fractal system IFS model representative of the dotspectrogram, determining affine parameters for IFS model, and thenmapping the dot spectrogram onto the viral diffusion curve using theIFS. Before the dot spectrograms is mapped to the viral diffusion curve,the dot spectrograms are interferometrically enhanced. After themapping, any uncertainty in the mapped coordinates is compensated forusing non-linear information filtering.

[0019] In accordance with a second aspect of the invention, a method isprovided for determining the viral load within a biological sample byanalyzing an output pattern of a biochip to which the sample is applied.In accordance with the method, a viral diffusion curve associated with atherapy of interest is generated and then calibrated using at least twoviral load measurements. Then the output pattern for the sample ismapped to coordinates on the calibrated viral diffusion curve usingfractal filtering. The viral load is determined from the calibratedviral diffusion curve by interpreting the coordinates of the viraldiffusion curve.

[0020] Apparatus embodiments are also provided. By exploiting aspects ofthe invention, disease management decisions related to diseaseprogression, therapy and dosage effectiveness may be made by trackingthe coordinates on the viral diffusion curve as successiveDNA-/RNA-based microarray samples are collected and analyzed.

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The features, objects, and advantages of the present inventionwill become more apparent from the detailed description set forth belowwhen taken in conjunction with the drawings in which like referencecharacters identify correspondingly throughout and wherein:

[0022]FIG. 1 is a flow chart illustrating an exemplary method fordetermining the effectiveness of a viral therapy in accordance with theinvention.

[0023]FIG. 2 is a flow chart illustrating an exemplary method forgenerating Viral Diffusion Curves for use with the method of FIG. 1.

[0024]FIG. 3 is a flow chart illustrating an exemplary method formapping dot spectrograms onto Viral Diffusion Curves using fractalfiltering for use with the method of FIG. 1.

[0025]FIG. 4 is a block diagram illustrating the effect of the fractalfiltering of FIG. 3.

[0026]FIG. 5 is a flow chart illustrating an exemplary method forcompensating for uncertainty using non-linear information filtering foruse with the method of FIG. 1.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

[0027] With reference to the figures, exemplary method embodiments ofinvention will now be described. The exemplary method will be describedprimarily with respect to the determination of changes in viral loadsbased upon the output patterns of a hybridized biochip microarray usingDNA samples, but principles of the invention may be applied to otherprotein-based samples or to other types of output patterns as well.

[0028] With reference to FIG. 1, steps will be described for generatingviral diffusion curves for use is processing DNA biomicroarray outputpatterns to determine the effectiveness of therapies imposed upon apatient providing samples for which the outputs are generated. Then,steps will be described for processing the specific output patternsusing the VDC's.

[0029] An underlying clinical hypothesis of the exemplary method is thatantiviral treatment should inhibit viral replication and lower anindividual's viral load from baseline or suppress rising values. Astationary or rising viral load after the introduction of antiviraltherapy indicates a lack of response to the drug(s) or the developmentof drug resistance. The VDC exploits the underlying hypothesis in partby correlating the rate of disease progression to a sample point valuesuch that a change in sample point indicates progression.

The Method

[0030] At step 100, parameters representative of viral load studies forthe therapy of interest are input. A preliminary viral diffusion curveis generated, at step 102, based upon the viral load studies. Theparameters representative of the viral load studies include baselineviral load (BVL) set point measurements at which detection is achieved,BVL at which therapy is recommended and viral load markers at whichdosage therapy is recommended. At step 104, a degree of directionalcausality in the preliminary viral diffusion curve is calibrated toyield the final viral diffusion curve.

[0031] Steps 100-104 are performed off-line for setting up the VDC's.These steps need be performed only once for a given therapy and for agiven set of baseline viral load measurements. Thereafter, any number ofDNA biomicroarray output patterns may be processed using the VDC's todetermine the effectiveness of the therapy. Preferably, VDC's aregenerated for an entire set of therapies that may be of interest suchthat, for any new DNA biomicroarray output pattern, the effectiveness ofany of the therapies can be quickly determined using the set of VDC's.In general, the aforementioned steps need be repeated only to update theVDC's based upon new and different baseline viral load studies or if newtherapies of interest need to be considered.

[0032] In the following, steps will be summarized for processing DNAbiomicroarray output patterns using the VDC's to determine whether anytherapies of interest represented by the VDC's are effective. Todetermine the effectiveness of therapy at least two samples of DNA to beanalyzed are collected from a patient, preferably taken some time apart,and biomicroarray patterns are generated therefrom. In other casesthough, the different samples are collected from different patients.

[0033] The output patterns for the DNA biomicroarray are referred toherein as dot spectrograms. A dot spectrogram is generated using a DNAbiomicroarray for each sample from an N by M DNA biomicroarray. Anelement of the array is an “oxel”: o(i,j). An element of the dotspectrogram is a hixel: h(i,j). The dot spectrogram is represented bycell amplitudes given by Φ(i,j) for i: 1 to N, and j: 1 to M.

[0034] Dot spectrograms are generated from the samples taken atdifferent times using a prefabricated DNA biomicroarray at step 106. Thedot spectrograms are interferometrically enhanced at step 108. Each dotspectrogram is then mapped to coordinates on the viral diffusion curvesusing fractal filtering at step 110. After the mapping, any uncertaintyin the mapped coordinates is compensated for at step 112 usingnon-linear information filtering.

[0035] VDC coordinates are initialized at step 114, then updated inaccordance with filtered dot spectrograms at step 116. A degree ofconvergence between the mapped coordinates on the viral diffusion curvesis then determined at step 118 and a determination is made as to whetherthe therapy of interest has been effective. The determination is basedupon whether the degree of convergence increases from one DNA sample toanother. An increase in degree of convergence is representative of alack of effectiveness of the therapy of interest. Hence, if the degreeof convergence decreases, then execution proceeds to step 120, wherein asignal is output indicating that the therapy is effective. If the degreeof convergence increases, then execution proceeds to step 122 whereinVDC temporal scale matching is performed. Then a determination is madeat step 124 whether an effectiveness time scale has been exceeded. Ifexceeded, then a conclusion is drawn that the effectiveness of the viraltherapy cannot be established even if more samples are analyzed. If notexceeded, then execution returns to step 106 wherein another sampletaken from the same patient at a latter time is analyzed by repeatingsteps 106 through 118.

Viral Load Studies

[0036] Viral load studies for therapies of interest are parameterized atstep 100 as follows. The therapy of interest is selected from apredetermined list of therapies for which viral load studies have beenperformed. Measurements from viral load studies are input for therapy ofinterest. As noted, the viral load measurements include one or more ofBaseline Viral Load (BVL) set point measurements at which detection isachieved; BVL at which therapy is recommended; and VL markers at whichdosage change recommended.

[0037] Data for the viral load measurements are obtained, for example,from drug qualification studies on a minimum include dosages, virallimits as well as time cycles within which an anti-viral drug is deemedeffective. The data is typically qualified with age/weight outliers andpatient history. Attribute relevant to this claim is the γ₁ or BVL_(LOW)which corresponds to the lowest detection limit shown for a therapy tobe effective using conventional assays or any other diagnostic means.BVL_(NP-LOW) denotes the lowest threshold at which viral load isachieved using a nucleotide probe. Using interferometric enhancementtechnique, BVL_(NP-LOW)<<BVL_(LOW).

Generation of Viral Diffusion Curves

[0038] Referring now to FIG. 2, the viral diffusion curves are generatedas follows. An equation is selected for representing the VDC at step200. Expectation (μ) and mean response parameters are determined at step202 for use in parameterizing the selected equation. Then the equationselected to represent the VDC is parameterized at step 204 to yield anumerical representation of the VDC. These steps will now be describedin greater detail.

[0039] These steps populate a canonical machine representation, denotedas VDC(i, Γ, γ, κ) (which is a special case of Fokker-Planck equation)to calibrate responses from a viral load detection DNA-array basedhybridization biomicroarray.

[0040] i is the index for a diagnostic condition/therapy of interest,

[0041] Γ denotes the parameter vector characterizing the VDC,

[0042] λ denotes the clinical endpoints vector that indicatesdetectability thresholds for a specific DNA-hybridization arrayimplementation

[0043] κ correspond to the uncertainty interval estimates.

[0044] An example of an equation selected for representing the VDC is:$\begin{matrix}{{\frac{\partial\rho}{\partial t} = {{{div}\left( {{\nabla{\Psi (x)}}\rho} \right)} + \frac{\Delta\rho}{\beta}}},} & {{\rho \left( {x,0} \right)} = {\rho^{0}(x)}}\end{matrix}$

[0045] The potential Ψ(x):

^(n)→[0, ∞) is a smooth function, β>0 is selected constant, and ρ⁰(x) isa probability density on

^(n).

[0046] Preferably, the diffusion potential of the equation and the BVLdata are such that:

Ψ(x)<c[BVL _(NP) _(—) _(LOW|) BVL _(LOW)]

[0047] the constant c is generally set to$c = \frac{\left\lbrack {{number}\quad {of}{\quad \quad \quad}{amplitude}\quad {discretization}{\quad \quad}{levels}} \right\rbrack}{\left\lbrack {{\log \left( {{PCR}\quad {amplification}\quad {factor}} \right)}^{*}{{avg}\left( {{oligonucleotides}/{oxel}} \right)}^{*}\left\lceil {{tagging}\quad {efficiency}} \right\rceil^{*}\left\lfloor {{binding}\quad {efficiency}} \right\rfloor} \right\rbrack}$

[0048] Binding efficiency is difficult to quantify analytically for abiomicroarray device technology. Hence, for use in the above equation,an estimate of the binding efficiency is preferably employed. A bindingefficiency of 30% (0.3) is appropriate, though other values mayalternatively used. Depending upon the specific biomicroarray used, theconstant c typically ranges between 0.0001 to 0.5.

Expectation and Mean Response Parameters

[0049] The expectation (μ) and mean response parameters are thendetermined at step 202 for use in parameterizing the equation selectedto represent the VDC. The expectation and mean response values aredetermined by: 1) performing conventional PCR amplification; 2)obtaining calibrated viral counts from the PCR amplification; 3)determining enhanced and normalized hybridization amplitude mean andvariance values corresponding to the calibrated viral counts; and 4)matching the enhanced and normalized hybridization amplitude mean andvariance values.

[0050] Two synthetic amplification techniques (in addition to PCR andany designer tagging) are used to achieve VL estimation above the BVLlimit set for the exemplary embodiment of the method, namely (a) readoutpre-conditioning, and (b) nonlinear interferometric enhancement.Moreover, the expectation match condition implies that:$\frac{{{Expectation}\quad\left\lbrack {{Log}\left( \left\lfloor {{interferometrically}{\quad \quad}{enhanced}{\quad \quad}{image}} \right\rfloor \right)} \right\rbrack}_{\bigvee{\lbrack{{expression}{\quad \quad}{set}\quad {of}{\quad \quad}{interest}}\rbrack}}\quad}{{{Expectation}{\quad \quad}\left\lbrack {{preconditioned}\quad {image}\quad {amplitude}} \right\rbrack}_{\bigvee{\lbrack{{expression}{\quad \quad \quad}{set}\quad {of}\quad {interest}}}}} \cong 1$

[0051] Variance matching is done similarly with respect to biomicroarrayreadout. The lower bound of mean response value can be given by:$\frac{\left( {{Variance}\quad\left\lbrack {{Log}\left( \left\lfloor {{interferometrically}\quad {enhanced}{\quad \quad \quad}{image}} \right\rfloor \right)} \right\rbrack}_{\bigvee{\lbrack{{expression}{\quad \quad}{set}{\quad \quad}{of}\quad {interest}}\rbrack}} \right.}{\left\lbrack {{preconditioned}\quad {image}{\quad \quad}{amplitude}} \right\rbrack_{\bigvee{\lbrack{{expression}\quad {set}\quad {of}\quad {interest}}}}} \cong {1\quad {Variance}}$

[0052] Using the above expression, a conservative lower bound forinterferometric enhancement is estimated for each nucleotide expressionof interest. Since the array fabrication device is assumed to have (i)an identical oligonucleotide density per oxel and (ii) equal lengtholigonucleotides, the same mean response amplitude can be assumed. Ifthese two assumptions are not met then bounds need to be individuallycalculated and averaged using the above formula. Another assumption isthat the binding efficiency is statistically independent of the actualoligonucleotide sequence. If this assumption does not hold for thespecific device technology then the binding efficiency should beprovided as well for each expressed sequence of interest. So thecomputational analysis method uses the analytically derived lowerbounds, as computed using the above equation. This is a one-timecalculation only and is done offline at design time.

Parameterization of the VDC

[0053] The equation selected to represent the VDC is then parameterizedusing the expectation and mean response values at step 204 to yield anumerical representation of the VDC using

y(x)=β₀+β₁ x+β ₂ x ²

[0054] subject to constraints$\overset{.}{x} = {{\gamma \quad {\sin^{k}\left\lbrack {\frac{\sqrt{\omega}}{\alpha}\left( {\beta_{0} + {\beta_{1}x} + {\beta_{2}x^{2}}} \right)} \right\rbrack}\sin \quad \omega \quad t} + {ɛ(t)}}$

[0055] with constants α, β, γ and ε<<1.

[0056] This utility of this parameterization is established as follows.The VDC canonical representation is based on a variational formulationof the Fokker-Planck. The Fokker-Planck (FP) equation, or forwardKolmogorov equation, describes the evolution of the probability densityfor a stochastic process associated with an Ito stochastic differentialequation. The exemplary method exploits the VDC to model a physicaltime-dependent phenomena in which randomness plays a major role. Thespecific variant used herein is one for which the drift term is given bythe gradient of a potential. For a broad class of potentials (thatcorrespond to statistical variability in therapy response), a timediscrete, iterative variational is constructed whose solutions convergeto the solution of the Fokker-Planck equation. The time-step is governedby the Wasserstein metric on probability measures. In this formulationthe dynamics may be regarded as a gradient flux, or a steepest descentfor the free energy with respect to the Wasserstein metric. Thisparameterization draws from theory of stochastic differential equations:wherein a (normalized) solution to a given Fokker-Planck equationrepresents the probability density for the position (or velocity) of aparticle whose motion is described by a corresponding Ito stochasticdifferential equation (or Langevin equation). The drift coefficient is agradient. The method exploits “designer conditions” on the drift anddiffusion coefficients so that the stationary solution of aFokker-Planck equation satisfies a variational principle. It minimizes acertain convex free energy functional over an appropriate admissibleclass of probability densities.

[0057] A physical analogy is to an optimal control problem which isrelated to the heating of a probe in a kiln. The goal is to control theheating process in such a way that the temperature inside the probefollows a certain desired temperature profile. The biomolecular analogyis to seek a certain property in the parameterized VDC—namely, anexponential jump in the VDC coordinate position for “small linearchanges in the viral count”.

[0058] This method is in contradistinction to conventional calibrationstrategies which obtain a linear or superlinear shift in quantizationparameter for an exponential shift in actual viral count.

[0059] As noted, the form of FP equation chosen is $\begin{matrix}{{\frac{\partial\rho}{\partial t} = {{{div}\left( {{\nabla{\Psi (x)}}\rho} \right)} + \frac{\Delta\rho}{\beta}}},} & {{\rho \left( {x,0} \right)} = {\rho^{0}(x)}}\end{matrix}$

[0060] where the potential Ψ(x):

^(n)→[0, ∞) is a smooth function, β>0 is selected constant, and ρ⁰(x) isa probability density on

^(n). The solution ρ(t,x) is a probability density on

^(n) for almost every fixed time t. So the distribution ρ(t,x)≧0 foralmost every (t,x)∈(0,∞)×

^(n), and ∫_(ℜ^(n))ρ(t, x)x = 1

[0061] .for almost every t, ∈(0,∞).

[0062] It is reasonably assumed that hybridization array device physicsfor the DNA biomicroarray (i.e., corresponding to the potential Ψ) hasan approximately linear response to the nucleotide concentration and theresponse is monotonic with bounded drift. So,${\rho_{s}(x)} = {\frac{1}{Z}^{({- {{\beta\Psi}{(x)}}})}}$

[0063] where the partition function Z is given byZ = ∫_(ℜ^(n))^((−βΨ(x)))  x

[0064] In this model the basis for device physics design is that thepotential needs to be modulated such that it grows rapidly enough for Zto be finite. This is not achieved by conventional methods. However, atechnique which does achieve this result is described in co-pending U.S.patent application Ser. No. 09/253,789, now U.S. Pat. No. 6,136,541,filed contemporaneously herewith, entitled “Method and Apparatus forAnalyzing Hybridized DNA Microarray Patterns Using Resonant InteractionsEmploying Quantum Expressor Functions”, which is incorporated byreference herein.

[0065] The probability measure ρ_(s)(x)dx is the unique invariantmeasure for the Markov random field (MRF) fit to the empirical viralload data.

[0066] The method exploits a special dynamical effect to design ρ. Themethod restricts the FP equation form above to a more restricted case:random walk emulating between critical equilibrium points.

[0067] To aid in understanding this aspect of the invention, considerthe diffusion form$\frac{\partial{\rho \left( {x,t} \right)}}{\partial t} = {\frac{1}{2}\quad D^{2}\quad \frac{\quad {\partial^{2}{\rho \left( {x,t} \right)}}}{\partial^{2}t}}$

[0068] where D²=πα²

[0069] and α is constant.

[0070] A specific VDC shape is parameterized by:

y(x)=β₀+β₁ x+β ₂ x ²

[0071] subject to constraints$\overset{.}{x} = {{\gamma \quad {\sin^{k}\left\lbrack {\frac{\sqrt{\omega}}{\alpha}\left( {\beta_{0} + {\beta_{1}x} + {\beta_{2}x^{2}}} \right)} \right\rbrack}\sin \quad \omega \quad t} + {ɛ(t)}}$

[0072] with constants α, β, γ and ε<<1.

[0073] These constants are set based upon the dynamic range expected forthe viral load. Thus, if the viral load is expected to vary only withina factor of 10, the constants are set accordingly. If the viral load isexpected to vary within a greater range, different constants areemployed. The actual values of the constants also depend upon theparticular disease.

[0074] Where the following conditions are met

[0075] Expectation match: E(x) = ∫_(−∞)^(∞)xf(x)x = μ

[0076] Variance: σ² = ∫_(−∞)^(∞)(x − μ)²f_(x)x

[0077] And ∫_(−∞)^(∞)f(x) = 1

[0078] The expectation and mean response parameters for use in theseequations are derived, as described above, from matching the enhancedand normalized hybridization amplitude mean and variance that correspondto calibrated viral counts (via classical PCR amplification).

[0079] A distribution represented by the above-equations then satisfiesthe following form with a prescribed probability distribution$\overset{.}{x} = {{\gamma \quad {\sin^{k}\left\lbrack {\frac{\sqrt{\omega}}{\alpha}{y(x)}} \right\rbrack}\sin \quad \omega \quad t} + {ɛ(t)}}$

[0080] Assuming:${y^{\prime} = {\frac{y}{x} > \beta > 0}},\quad {\beta = {constant}}$

[0081] and ε(t)=ε₀ay

[0082] such that

{dot over (a)}=a ^(1/3)(y−1)(y+1)−ε₀ a

[0083] and the distribution controlling equation is

f(x)=0.5|y′(x)|

[0084] such that y(−1)<X<y(1).

[0085] The characteristic timescale of response for this system is givenby$T^{*} = {\frac{1}{\omega}{arc}\quad {\cos \left\lbrack {1 - {\frac{B\left( {{1/3},{1/3}} \right)}{\sqrt[3]{2}}\frac{\alpha \sqrt{\omega}}{\gamma}}} \right\rbrack}}$

[0086] the successive points must show a motion with characteristictimescale. The VDC is designed such that sampling time falls well withincharacteristic time.

[0087] As noted the actual information used for populating above theparameters is available from the following: Baseline viral load (BVL)set point measurements at which detection is achieved; BVL at whichtherapy is recommended; and VL markers at which dosage changerecommended.

[0088] The following provides an example of preclinical data that isavailable to to assist in parameterizing the VDC.

NOTIONAL VIRAL LOAD MANAGEMENT EXAMPLE

[0089] This is a synthetic example to illustrate how data from clinicalstudies may be used to calibrate the VDC.

[0090] Viral Load analysis studies, using conventional assays, in HIVprogression have shown that neither gender, age, HCV co-infection, pasthistory of symptomatic HIV-1 infection, duration of HIV-1 infection norrisk group are associated with a higher risk of increasing baselineviral load (BVL) to the virologic end-point. However, patients with ahigh (BVL) between 4000-6000 copies had a 10-fold higher risk ofincreasing the level of viral load than patients with a BVL below 1500copies/ml. Thus, baseline viral load set point measurements provide animportant indicator for onset of disease.

[0091] Initiation of antiretroviral therapy is generally recommendedwhen the CD4⁺ T-cell count is <600 cells/mL and the viral load levelis >6,000 copies/mL. When the viral load is >28000 copies/mL, initiationof therapy is recommended regardless of other laboratory markers andclinical status.

[0092] Effective antiretroviral treatment may be measured by changes inplasma HIV RNA levels. The ideal end point for effective antiviraltherapy is to achieve undetectable levels of virus (<400 copies/mL). Adecrease in HIV RNA levels of at least 0.5 log suggests effectivetreatment, while a return to pretreatment values (±0.5 log) suggestsfailure of drug treatment.

[0093] When HIV RNA levels decline initially but return to pretreatmentlevels, the loss of therapy effectiveness has been associated with thepresence of drug-resistant HIV strains.

[0094] The therapy-specific preclinical viral load markers (such as lowand high limits in the above example) are used to establish actual BVLboundaries for the VDC associated with a particular therapy. In thisregard, the deterimination of the BVL parameters is disease specific.For example, in HIV methods such as RT-PCR, bDNA or NASBA are used.Other diseases use other assays. Typically, once the parameters of theVDC equation have been set (i.e. constants α, β, γ and ε), only twoviral load markers are needed to complete the parameterization of theVDC. This is in contrast to previous techniques whereby expensive andlaborious techiques are required to determine the shape of a viraldiffusion curve. The present invention succeeds in using only two viralload markers in most cases by exploiting the canonical VDC describedabove which has predefined properties and which is predetermined basedupon the particular biochip being used.

Calibration of Viral Diffusion Curves

[0095] Referring again to FIG. 1, the directional causality of the VDCis calibrated at step 104 in the context of an NIF discussed in greaterdetail below. At least arbitrarily selected three sample points are usedexecute the NIF calibration computation. The resulting polynomial isused to extracting qualitative coherence properties of the system.

[0096] The spectral [Θ] and temporal coherence [

] is incrementally estimated and computed for eachmutation/oligonucleotide of interest by a NIF forward estimationcomputation (described further below). The two estimates are normalizedand convolved to yield cross-correlation function over time. The shapeindex (i.e., curvature) of the minima is used as a measure fordirectional causality. Absence of curvature divergence is used to detecthigh directional causality in the system.

Sample Collection

[0097] Samples are collected at step 106 subject to a sample pointcollection separation amount. The separation amount for two samples ispreferably within half a “drug effectiveness mean time” covering 2σpopulation level wherein a denotes the standard deviation in periodbefore which a effectiveness for a particular drug is indicated. Thefollowing are some general guidelines for sample preparation for usewith the exemplary method:

[0098] It is important that assay specimen requirements be strictlyfollowed to avoid degradation of viral RNA.

[0099] A baseline should be established for each patient with twospecimens drawn two to four weeks apart.

[0100] Patients should be monitored periodically, every three to fourmonths or more frequently if therapy is changed. A viral load level thatremains at baseline or a rising level indicates a need for change intherapy.

[0101] Too much significance should not be given to any one viral loadresult. Only sustained increases or decreases of 0.001-0.01 log[conventional methods typically require a 0.3-0.5 log change] or moreshould be considered significant. Biological and technical variation ofup to 0.01 log [typical conventional limit: 0.3 log] is possible. Also,recent immunization, opportunistic infections and other conditions maycause transient increases in viral load levels.

[0102] A new baseline for each patient should be established whenchanging laboratories or methods.

[0103] Recommendations for frequency of testing are as follows:

[0104] establish baseline: 2 measurements, 2 to 4 weeks apart

[0105] every 3 to 4 months or in conjunction with CD4⁺ T-cell counts

[0106] 3 to 4 weeks after initiating or changing antiretroviral therapy

[0107] shorter intervals as critical decisions are made.

[0108] measurements 2-3 weeks apart to determine a baseline measurement.

[0109] repeat every 3-6 months thereafter in conjunction with CD4 countsto monitor viral load and T-cell count.

[0110] avoid viral load measurements for 3-4 weeks following animmunization or within one month of an infection.

[0111] a new baseline for each patient should be established whenchanging laboratories or methods.

[0112] The samples are applied to a prefabricated DNA biomicroarray togenerate one or more dot spectrograms each denoted Φ(i,j) for i: 1 to N,and j: 1 to M. The first sample is referred to herein as the k=1 sample,the second as the k=2 sample, and so on.

Interferometric Enhancement of the Dot Spectrogram

[0113] Each dot spectrogram provided by the DNA biomicroarray isfiltered at step 108 to yield enhanced dot spectrograms Φ(κ) either byperforming a conventional Nucleic Assay Amplification or by applyingpreconditioning and normalization steps as described in the co-pendingpatent application having Ser. No. 09/253,789, now U.S. Pat. No.6,136,541, entitled “Method And Apparatus For Analyzing HybridizedBiochip Patterns Using Resonance Interactions Employing QuantumExpressor Functions”. The application is incorporated by referenceherein, particularly insofar as the descriptions of the use ofpreconditioning and normalization curves are concerned.

Fractal Filtering

[0114] Each enhanced dot spectrogram is then mapped to the VDC usingfractal filtering at step 110 as shown in FIG. 3 by generating apartitioned iterated fractal system 302, determining affine parametersfor the IFS 304 and then mapping the enhanced dot spectrogram onto theVDC using the IFS, step 306.

[0115] The VDC representation models a stochastic process given by${{W(f)}\left( {x,y} \right)} = \left\{ \begin{matrix}{{{\gamma_{i} \cdot {f\left( {{\frac{1}{\sigma_{i}}\left( \frac{x - x_{D}^{i}}{y - y_{D}^{i}} \right)} + \frac{x_{R}^{i}}{y_{R}^{i}}} \right)}} + {\tau \left( \frac{x - x_{D}^{i}}{y - y_{D}^{i}} \right)} + \beta_{i}},} \\{{{{if}\quad \left( {x,y} \right)} \in {\mu_{i}^{- 1}(1)}},{{{{for}\quad {some}\quad 1} \leq i \leq m};}} \\{0,\quad {{otherwise};}}\end{matrix} \right.$

[0116] for any (x,y)∈

² and f∈

(

²)

[0117] An exemplary partitioned iterated fractal system (IFS) model forthe system is

W={Φ _(i)=(μ_(i) ,T _(i))}i=1,2, . . . ,m

[0118] where the affine parameters for the IFS transformation are givenby$T_{i} = \left( {\left( {x_{D}^{i},y_{D}^{i}} \right),\left( {x_{R}^{i},y_{R}^{i}} \right),{\sigma_{i} = \begin{pmatrix}s_{00}^{i} & s_{01}^{i} \\s_{10}^{i} & s_{11}^{i}\end{pmatrix}},{\tau_{i} = \left( {t_{0}^{i},t_{1}^{i}} \right)},\gamma_{i},\beta_{i},} \right)$

[0119] where the D-origin is given by (x_(D) ^(i),y_(D) ^(i)),

[0120] the R-origin is given by (x_(R) ^(i),y_(R) ^(i))

[0121] spatial transformation matrix is given by ρ_(i)

[0122] the intensity tilting vector is given by τ_(i)

[0123] the contrast adjuctment is given by γ_(i,)

[0124] the brightness adjustment is given by β_(i,)

[0125] and wherein Φ represents the enhanced dot spectrogram and whereinμ represents the calculated expectation match values

[0126] This IFS model maps the dot spectrogram to a point on the VDCwherein each VDC coordinate is denoted by VDC(t,Θ) such that

W[Φ, k]→VDC(k, Θ)

[0127] Wherein k represents a sample.

[0128] In the above equation, Θ represent the parameters of the IFS map.

[0129] Thus the output of step 110, is a set of VDC coordinates,identified as VDC(k, Θ), with one set of coordinates for each enhanceddot spectrogram k=1, 2 . . . n.

[0130] The effect of the steps of FIG. 3 is illustrated in FIG. 4 whichshows a set of dot spectrograms 450, 451 and 452 and a VDC 454. Asillustrated, each dot spectrogram is mapped to a point on the VDC.Convergence toward a single point on the VDC implies ineffectiveness ofthe viral therapy. A convergence test is described below.

Uncertainty Compensation

[0131] With reference to FIG. 5, any uncertainty in the coordinatesVDC(k, Θ) is compensated using Non-linear Information Filtering asfollows. Biomicroarray dispersion coefficients, hybridization processvariability values and empirical variance are determined at step 402.The biomicroarray dispersion coefficients, hybridization processvariability values and empirical variance are then converted at step 404to parameters for use in NIF. The NIF is then applied at step 406 to theVDC coordinates generated at step 106 of FIG. 1.

[0132] Nonlinear information filter (NIF), is a nonlinear variant of theExtended Kalman Filter. A nonlinear system is considered. Linearizingthe state and observation equations, a linear estimator which keepstrack of total state estimates is provided. The linearized parametersand filter equations are expressed in information space. This gives afilter that predicts and estimates information about nonlinear stateparameters given nonlinear observations and nonlinear system dynamics.

[0133] The information Filter (IF) is essentially a Kalman Filterexpressed in terms of measures of the amount of about the parameter ofinterest instead of tracking the states themselves, i.e., track theinverse covariance form of the Kalman filter. Information here is in theFisher sense, i.e. a measure of the amount of information about aparameter present in the observations.

[0134] Uncertainty bars are estimated using NIF algorithm. Theparameters depend on biomicroarray dispersion coefficients,hybridization process variability and empirical variance indicated inthe trial studies.

[0135] One particular advantage of the method of the invention is thatit can also be used to capture the dispersion from individual toindividual, therapy to therapy etc. It is extremely useful and enablingto the method in that it can be apriori analytically set to a prechosenvalue and can be used to control the quality of biomicroarray outputmapping to VDC coordinates.

[0136] The biomicroarray dispersion coefficients, hybridization processvariability values and empirical variance are determined as follows.Palm generator functions are used to capture stochastic variability inhybridization binding efficacy. This method draws upon results instochastic integral geometry and geometric probability theory.

[0137] Geometric measures are constructed to estimate and bound theamplitude wanderings to facilitate detection. In particular we seek ameasure for each mutation-recognizer centered (MRC-) hixel that isinvariant to local degradation. Measure which can be expressed bymultiple integrals of the form m(Z) = ∫_(Z)f(z)z

[0138] where Z denotes the set of mutations of interest. In other words,we determine the function f(z) under the condition that m(z) should beinvariant with respect to all dispersions ξ. Also, up to a constantfactor, this measure is the only one which is invariant under a group ofmotions in a plane. In principle, we derive deterministic analyticaltransformations on each MRC-hixel., that map error-elliptic dispersionbound defined on

² (the two dimension Euclidean space—i.e., oxel layout) onto measuresdefined on

. The dispersion bound is given by

Log₄(Ô _((i,j))|^(Z)).

[0139] Such a representation of uniqueness facilitates the rapiddecimation of the search space. It is implemented using a filterconstructed using measure-theoretic arguments. The transformation underconsideration has its theoretical basis in the Palm Distribution Theoryfor point processes in Euclidean spaces, as well as in a new treatmentin the problem of probabilistic description of MRC-hixel dispersiongenerated by a geometrical processes. Latter is reduced to a calculationof intensities of point processes. Recall that a point process in someproduct space E×F is a collection of random realizations of that spacerepresented as {(e_(i), f_(i)), |e_(I)∈E, f_(i)∈F}.

[0140] The Palm distribution, Π of a translation (T_(n)) invariant,finite intensity point process in

^(n) is defined to the conditional distribution of the process. Itsimportance is rooted in the fact that it provides a completeprobabilistic description of a geometrical process.

[0141] In the general form, the Palm distribution can be expressed interms of a Lebesgue factorization of the form

E _(P) N*=ΛL _(N)×Π

[0142] Where Π and Λ completely and uniquely determine the sourcedistribution P of the translation invariant point process. Also, E_(P)N* denotes the first moment measure of the point process and L_(N) is aprobability measure.

[0143] Thus a determination of Π and Λ is needed which can uniquelyencode the dispersion and amplitude wandering associated with theMRC-hixel. This is achieved by solving a set of equations involving PalmDistribution for each hybridization (i.e., mutation of interest). Eachhybridization is treated as a manifestation of a stochastic pointprocess in

^(2.)

[0144] In order to determine Π and Λ we have implemented the followingmeasure-theoretic filter:

[0145] Determination of Λ

[0146] using integral formulae constructed using the marginal densityfunctions for the point spread associated with MRC-hixel(i,j)

[0147] The oligonucleotide density per oxel ρ_(m(i,j)), PCRamplification protocol (σ_(m)), fluorescence binding efficiency (η_(m))and imaging performance ({overscore (ω)}_(m)) provide the continuousprobability density function for amplitude wandering in the m-thMRC-hixel of interest. Let this distribution be given by

(ρ_(m(i,j)), σ_(m), η_(m), {overscore (ω)}_(m)).

[0148] The method requires a preset binding dispersion limit to beprovided to compute Λ. The

(ρ_(m(i,j)), σ_(m), η_(m), {overscore (ω)}_(m))

[0149] second moment to the function

[0150] at SNR=0 condition is used to provide the bound.

[0151] Determination of Π

[0152] Obtained by solving the inverse problem

Π=Θ*P

[0153] where P = ∫_(τ₁)^(τ₂)(ρ_(m(i, j)), σ_(m), η_(m), ϖ_(m)  )∂τ

[0154] where τ₁ and τ₂ represent the normalized hybridization dispersionlimits.

[0155] The number are empirically plugged in. The values of 0.1 and 0.7are appropriate for, respectively, signifying loss of 10%-70%hybridization. Also, Θ denotes the distribution of known point process.The form 1/(1+exp(

( . . . ))) is employed herein to represent Θ.

[0156] The biomicroarray dispersion coefficients, hybridization processvariability values and empirical variance are then converted toparameters at step 304 for use in NIF as follows.

[0157] The NIF is represented by:

[0158] Predicted State=f(current state, observation model, informationuncertainty, information model)

[0159] Detailed equations are given below.

[0160] In the biomicroarray context, NIF is an information-theoreticfilter that predicts and estimates information about nonlinear stateparameters (quality of observable) given nonlinear observations (e.g.,post hybridization imaging) and nonlinear system dynamics(spatio-temporal hybridization degradation). The NIF is expressed interms of measures of the amount of information about the observable(i.e., parameter of interest) instead of tracking the states themselves.It has been defined as the inverse covariance of the Kalman filter,where the information is in the Fisher sense, i.e, a measure of theamount of information about o_(I) present in the observations Z^(k)where the Fisher information matrix is the covariance of the scorefunction.

[0161] In a classical sense the biomicroarray output samples can bedescribed by the nonlinear discrete-time state transition equation ofthe form:

VDC(k)=f(VDC(k−1),Φ(k−1), k)+v(k)

[0162] where VDC(k−1) is the state at time instant (k−1),

[0163] Φ(k−1) is the input vector (embodied by dosage and/or therapy)

[0164] v(k) is some additive noise; corresponds to the biomicroarraydispersion as computed by the Palm Generator functions above.

[0165] VDC(k) is the state at time k,

[0166] f(k,.,) is the nonlinear state transition function mappingprevious state and current input to the current state. In this case itis the fractal mapping that provides the VDC coordinate at time k.

[0167] The observations of the state of the system are made according toa non-linear observation equation of the form

z(k)=h(VDC(k))+w(k)

[0168] where z(k) is the observation made at time k

[0169] VDC(k) is the state at time k,

[0170] w(k) is some additive observation noise

[0171] and h(.,k) is the current non-linear observation model mappingcurrent state to observations, i.e., sequence-by-hybridization made attime k,

[0172] v(k) and w(k) are temporally uncorrelated and zero-mean. This istrue for the biomicroarray in how protocol uncertainties, bindingdynamics and hybridization degradation are unrelated and additive. Theprocess and observation noises are uncorrelated.

E[v(i)w ^(T)(j)]=0, ∀ i,j.

[0173] The dispersion coefficients together define the nonlinearobservation model.

[0174] The nonlinear information prediction equation is given by

ŷ(k|k−1)=Y(k|k−1)f(k,{circumflex over (V)}DC(k−1|k−1),u(k−1))

Y(k|k−1)=[∇f _(x)(k)Y ⁻¹(k−1|k−1)∇f _(x) ^(T)(k)+Q(k)]⁻¹

[0175] The nonlinear estimation equations are given by

ŷ(k|k)=ŷ(k|k−1)+i(k)

Y(k|k)=Y(k|k−1)+I(k)

[0176] where

I(k)=∇h _(x) ^(T)(k)R ⁻¹(k)∇h _(x)(k)

i(k)=∇h _(x) ^(T)(k)R ⁻¹(k)[v(k)+∇h _(x)(k){circumflex over(V)}DC(k|k−1)]

[0177] where

v(k)=z(k)−h({circumflex over (x)}(k|k−1)).

[0178] In this method NIF helps to bind the variability in the VDCcoordinate mapping across sample to sample so that dosage and therapyeffectiveness can be accurately tracked.

[0179] The NIF is then applied to enhanced, fractal-filtered dotspectrogram at step 306 as follows. States being tracked correspond topost-hybridization dot spectrogram in this method. NIF computation asdescribed above specifies the order interval estimate associated with aVDC point. It will explain and bound the variability in Viral loadestimations for the same patient from laboratory to laboratory.

[0180] The NIF also specifies how accurate each VDC coordinate is giventhe observation model and nucleotide set being analyzed.

Convergence Testing

[0181] Referring again to FIG. 1, once any uncertainty is compensated,the VDC coordinates are renormalized at step 114. The renormalized VDCcoordinates are patient specific and therapy specific. Alternately thecoordinates could be virus/nucleotide marker specific. TheNIF-compensated VDC coordinates are renormalized to the first diagnosticsample point obtained using the biomicroarray. Thus a patient can bereferenced to any point on the VDC.

[0182] This renormalization step ensures that VDC properties aremaintained, notwithstanding information uncertainties as indicated bythe NIF correction terms. The approach is drawn from“renormalization-group” approach used for dealing with problems withmany scales. In general the purpose of renormalization is to eliminatean energy scale, length scale or any other term that could produce aneffective interaction with arbitrary coupling constants. The strategy isto tackle the problem in steps, one step for every length scale. In thismethod the renormalization methodology is abstracted and applied duringa posteriori regularization to incorporate information uncertainty andsample-to-sample variations.

[0183] This is in contradistinction to current viral load measurementcalibration methods that either generate samples with same protocol andsame assumptions of uncertainty or use some constant correction term.Both existing approaches skew the viral load readout so thatmeasurements are actually accurate only in a limited “information” and“observability” context. This explains the large variations in readingsfrom different laboratories and technicians for the same patient sample.

[0184] Specifically, we include the dynamic NIF correction function tothe gradient of the VDC at the sample point normalized in a manner suchthat when the information uncertainty is null, the correction termvanishes. As discussed in the above steps, the NIF correction terms isactually derived from the noise statistics of the microarray sample.

<VDC′(k,Θ)>=VDC(k,Θ)+[∇NIF(Y,I)_(k)]

[0185] where ∇NIF(Y,I)_(k) denotes the gradient of nonlinear informationprediction function. Under perfect observation model this term vanishes.

[0186] Once initialized, the VDC coordinates are then updated at step116 applying the IFS filter W[ ] on k+1th sample, by

VDC(k+1,Θ)←W[Biomicroarray Output, K+1];

[0187] A direction convergence test is next performed at step 118 todetermine whether the selected therapy has been effective. Ifconvergence establishes that the viral load for the patient is moving ina direction representative of a lower viral load, then the therapy isdeemed effective. The system is deemed to be converging toward a lowerviral load if and only if:${{\frac{{{VDC}\left( t_{k} \right)} - {{VDC}\left( t_{k - j} \right)}}{{{VDC}\left( t_{k - 1} \right)} - {{VDC}\left( t_{k - j} \right)}}} > {1\bigwedge{\frac{{VDC}_{peak} - {{VDC}\left( t_{k} \right)}}{{VDC}_{peak} - {{VDC}\left( t_{k - 1} \right)}}}} < 1}\quad$  for  k > 2  and  j > 0

[0188] The above relationships needs to be monotonically persistent forat least two combinations of k and j.

Also, date[k]−date[j]<κ*characteristic time, {haeck over (t)} (in days)

[0189] Where κ captures the population variability. Typically, κ<1.2.

[0190] The peak VDC value is determined based on the VDC. The peakamplitude is an artifact of the specific parameterization to theFokker-Planck equation used in deriving the VDC. It is almost alwaysderived independent of the specific sample.

[0191] In connection with step 118, a VDC Shift factor Δ may bespecified at which a dosage effectiveness decision and/or diseaseprogression decision can be made. The VDC shift factor is applied toestimate the VDC curvature traversed between two measurements.

[0192] If the system is deemed to be converging toward a lower viralload, an output signal is generated indicating that the therapy ofinterest is effective at step 120. If not, then the execution proceedsto step 122 wherein VDC scale matching is performed. A key assumptionunderlying this method is that movement along VDC is significant if andonly if the sample points are with a constant multiple of temporal scalecharacterizing the VDC. This does not in any way preclude thepharmacological relevance associated with the datapoints. But completepharmacological interpretation of the sample points is outside the scopeof this method. The process is assumed to be cyclostationary or at alarge time scale and two or more sample points have been mapped to VDCcoordinates. The coordinates are then plugged into an analytic toestimate the empirical cycle time ({haeck over (t)}). This isimplemented as described in the following sections.

[0193] Again the empirical cycle time ({haeck over (t)}) is used toestablish decision convergence.

Scale Matching

[0194] Select a forcing function of the form:

Ψ=

k.

^(m) cos ωt

[0195] where k is a constant and m is a small odd integer (m<7).

[0196] The phase space for this dynamical system is represented by:$\begin{matrix}{\overset{.}{x} = {\gamma \quad {\sin \left\lbrack {\frac{\sqrt{\omega}}{\alpha}{erf}\quad {m\left( \frac{x}{\sigma \sqrt{2}} \right)}} \right\rbrack}^{\frac{k}{k + 2}}\sin \quad \omega \quad t}} \\{where} \\{{{erf}\quad {m(x)}} = \left\{ \begin{matrix}{- 1} & {{{if}\quad x} < {- N}} \\{{erf}\quad (x)} & {{{if}\quad {\quad x}} \leq N} \\1 & {x > N}\end{matrix} \right.}\end{matrix}$

[0197] and erf m(.) denotes the error function.

[0198] K is set to 1; where o<α, γ, ω<1 are refer to constants.

[0199] Let τ_(emp) denote the cycle-time-scale for this empiricalsystem.

[0200] If log_(e)(τ_(emp) /T)>1 (in step 10) then we claim thattime-scales do not match.

Time Scale Testing

[0201] Next a determination has been made as to whether an effectivenesstimescale has been exceeded at step 124 by:

[0202] Checking if a time step between successive sampling has exceededT by

[0203] determining if Time_(k+1)−Time_(k)>T

[0204] such that VDC(k+1, Θ)−VDC(k, Θ))<ζ where

[0205] is set to 0.0001 and wherein

[0206] T is given by$T^{*} = {\frac{1}{\omega}{\arccos \left\lbrack {1 - {\frac{B\left( {{1/3},{1/3}} \right)}{\sqrt[3]{2}}\frac{\alpha \sqrt{\omega}}{\gamma}}} \right\rbrack}}$

[0207] B(1/3,1/3) represents the Beta function around the coordinates(1/3,1/3), We can actually use all B(1/2i+1,1/2i+1) for i>1 and i<7.

[0208] If Time_(k+1)−Time_(k)>T then output signal at step 126indicating that either

[0209] no change in viral load concluded, OR

[0210] therapy deemed ineffective, OR

[0211] dosage deemed suboptimal.

[0212] If Time_(k+1)−Time_(k)<T then process another sample by repeatingall steps beginning with Step 4 wherein a dot spectrogram is generatedfor a new sample.

[0213] If the effectiveness time scale has been exceeded then a signalis output indicating that no determination can be as to whether thetherapy of interest is effective. If the time scale is not exceeded,then execution returns to step 106 for processing another sample. Ifavailable, and the processing steps are repeated.

Alternative Implementations

[0214] Details regarding a related implementation may be found inco-pending U.S. patent application Ser. No. 09/253,792, now U.S. Pat.No. 6,142,681, filed contemporaneously herewith, entitled “Method andApparatus for Interpreting Hybridized Bioelectronic DNA MicroarrayPatterns Using Self Scaling Convergent Reverberant Dynamics”, andincorporated by reference herein.

[0215] The exemplary embodiments have been primarily described withreference to flow charts illustrating pertinent features of theembodiments. Each method step also represents a hardware or softwarecomponent for performing the corresponding step. These components arealso referred to herein as a “means for” performing the step. It shouldbe appreciated that not all components of a complete implementation of apractical system are necessarily illustrated or described in detail.Rather, only those components necessary for a thorough understanding ofthe invention have been illustrated and described in detail. Actualimplementations may contain more components or, depending upon theimplementation, may contain fewer components.

[0216] The description of the exemplary embodiments is provided toenable any person skilled in the art to make or use the presentinvention. Various modifications to these embodiments will be readilyapparent to those skilled in the art and the generic principles definedherein may be applied to other embodiments without the use of theinventive faculty. Thus, the invention is not intended to be limited tothe embodiments shown herein but is to be accorded the widest scopeconsistent with the principles and novel features disclosed herein.

What is claimed is:
 1. A system for determining the level of abiological indicator within a patient sample applied to an arrayedinformation structure, where the arrayed information structure emitsdata indicative of the biological indicator, based on digitized outputpatterns from the arrayed information structure, comprising: apreconditioning unit for pre-conditioning the digitized output pattern;an interferometric unit configured to generate an interference betweenthe preconditioned digitized output pattern and a reference wave toenhance the digitized output pattern; and an analysis unit for analyzingthe interferometrically enhanced digitized output pattern to determinethe level of the biological indicator.
 2. A system for determining thelevel of specific constituents within an output pattern generated from adetected image of a biological sample applied to an array wherein theoutput pattern comprises signals associated with noise, and signalsassociated with the biological sample which have intensities bothgreater and less than intensities of signals associated with noise,comprising: tessellation means for tessellating the output pattern;signal processing means for amplifying signals associated with thebiological sample within the tessellated output pattern, having anintensity lower than the intensity of signals associated with noise, toan intensity greater than the intensity of the signals associated withnoise to generate a modified output pattern; first determination meansfor determining which signals within the modified output patterncorrelate with specific constituents within the biological sample;second determination means for determining specific constituents withinthe biological sample based on the signals within the modified outputpattern correlating to specific constituents within the biologicalsample; and third determination means for associating the signalscorrelating to specific constituents with levels of such specificconstituents within the sample.
 3. A system for quantitating specificconstituents within an output pattern generated from a detected image ofa biological sample applied to an array wherein the output patterncomprises signals associated with noise, and signals associated with thebiological sample which have intensities both greater and less thanintensities of signals associated with noise, comprising: a tessellationunit for segmenting the output pattern; a signal processing unit toamplify signals associated with the biological sample within thesegmented output pattern, having an intensity lower than the intensityof signals associated with noise, to an intensity greater than theintensity of the signals associated with noise to generate a modifiedoutput pattern; a first determination unit to determine which signalswithin the modified output pattern correlate with specific constituentswithin the biological sample; a second determination unit to determinespecific constituents within the biological sample based on the signalswithin the modified output pattern correlating to specific constituentswithin the biological sample; and a mapping unit for mapping the signalscorrelating to specific constituents on a diffusion curve to determinethe level of such specific constituents within the biological sample. 4.A technique for analyzing an output pattern of a biological sampleapplied to an array to determine the presence and quantity of specificconstituents within a biological sample applied to the array, whereinthe output pattern comprises signals associated with noise, and signalscorrelating to the biological sample with the signals correlating to thebiological sample having intensities both greater and less than thesignals associated with noise, the method comprising the steps of:segmenting the output pattern of the array using tessellation;interferometrically enhancing the segmented output pattern to amplifysignals associated with the biological sample, having an intensity lowerthan the intensity of signals associated with noise, to an intensitygreater than the intensity of the signals associated with noise togenerate a modified output pattern; associating signals within theinterferometrically enhanced segmented output pattern with specificconstituents within the biological sample; and determining specificconstituents within the biological sample based on the signals withinthe interferometrically enhanced segmented output pattern associatedwith specific constituents within the biological sample; and mapping thesignals associated with specific constituents to a diffusion curve.
 5. Acomputer code product that determines the presence of specificconstituents within an output pattern of a biological sample applied toan array of detectors, wherein the output pattern comprises signalsassociated with noise, and signals associated with the biological samplewhich have intensities both greater and less than intensities of signalsassociated with noise, the computer code product comprising: computercode that segments the output pattern using tessellation; computer codethat utilizes signal processing to amplify signals within the segmentedoutput pattern associated with the biological sample having an intensitylower than the intensity of the signals associated with noise, to anintensity greater than the intensity of the signals associated withnoise to generate a modified output pattern; computer code thatdetermines which signals within the modified output pattern correlatewith specific constituents within the biological sample; and computercode that determines specific constituents within the biological samplebased on the signals within the modified output pattern correlating tospecific constituents within the biological sample; and computer codethat maps signals correlating to specific constituents to a diffusioncurve.
 6. A method for determining the effectiveness of a therapy byanalyzing microarray output patterns generated from two or morebiological samples taken from a patient undergoing the therapycomprising the steps of: generating a diffusion curve with a therapy ofinterest; mapping the output patterns to the diffusion curve;determining the degree of convergence between the mapped coordinates ofthe respective output patterns mapped on the diffusion curve.
 7. Themethod of claim 6 further comprising the step of interferometricallyenhancing the output patterns prior to the mapping step.
 8. The methodof claim 7 wherein the interferometric enhancement step utilizesresonance interferometry.
 9. The method of claim 8 wherein the resonanceinterferometry is either quantum resonance interferometry or stochasticresonance interferometry.
 10. The method of claim 7 further comprisingthe step of tessellating the output pattern prior to the interferometricenhancement step.
 11. The method of claim 6 further comprising the stepof performing nucleic acid amplification to enhance the output patternsprior to the mapping step.
 12. The method of claim 6 wherein the sampleis selected from a group consisting of DNA, RNA, protein,peptide-nucleic acid (PNA) and targeted nucleic acid (TNA) samples.